Day 7 sept 12 mid chapter 1 check.notebook - …mrsdempseysmathsite.weebly.com/.../day_7_sept_12_… · · 2014-09-12Day 7 sept 12 mid chapter 1 check.notebook 3 ... H.O.T. Problems

Day7sept12midchapter1check.notebook

1

September12,2014

Jun192:48PM Sep138:38AM

May1310:32AM May1310:32AM



2

September12,2014



Jun192:47PM Jun192:47PM


3

September12,2014



Jun192:47PM May1310:36AM

In-class assignment: Complete the mid-chapter 1 check. You will take a 9 question quiz today.


4

September12,2014

May1310:36AM

Case1

May1310:36AM

Case2




5

September12,2014

Jun192:48PM

Attachments

14_Powers_of_Monomials.pdf

MidChapter_Check2.pdf

Simplify using the Laws of Exponents.

1.(42)3

SOLUTION:To find the power of a power, multiply the exponents. Simplify.

2.(53)3


3.(d7)6


4.(h4)9


5.[(32)2]2


6.[(52)2]2


7.(5j6)4


8.(11c4)3


9.(6a2b

6)3


10.(2m5n11)6


11.(3w3z

8)5


12.(5r4s12)4


13.A shipping box is in the shape of a cube. Each side

measures 3c6d

2 inches. Express the volume of the

cube as a monomial.

SOLUTION:

The formula for the volume of a cube is V = s3,

where x is the length of each side. Write the expression for the volume using the side length

3c6d

2. Then simplify.

The volume of the box is 27c18d6 cubic units.

14.Tamara is decorating her patio with a planter in the shape of a cube like the one shown. Find the volume of the planter.

SOLUTION:


where x is the length of each side. Write the

expression for the volume using the side length 3w4.

Then simplify.

The volume of the box is 27w

12 cubic units.

Copy and Solve Simplify. Show your work on a separate sheet of paper.

15.


16.


17.(2v7)3(4v2)4

SOLUTION:To find the power of a power, multiply the exponents. Group the numbers and the variables. Simplify.

18.Identify Structure Draw a line connecting the Law(s) of Exponents you would use to simplify each of the expressions. Then simplify each one.

SOLUTION:Examine each of the expressions.

(a9)3

A power is raised to a power, use the Power

ofaPowerlaw.

(m8) ( m4) The expression involves division and

exponents, so use the Quotient of Powers law

5x2(7x

4)The expression involves multiplication

and exponents, so use the Product of Powers

law.5x2(7x4)=5(7)x2 + 4 or 35x6

The numerator involves a product raised to

a power, so use the Power of a Product law. The expression involves division and exponents, so use theQuotientofPowerslaw.

(n6)8


ofaPowerlaw.(n6)8= n68 or n48

19.Reason Inductively The table gives the area and volume of a square and cube, respectively, with side lengths shown.

a. Complete the table. b. Describe how the area and volume are each affected if the side length is doubled. Then describe how they are each affected if the side length is tripled.

SOLUTION:a.

b. If the side length is doubled, the area is quadrupledand the volume is multiplied by 8. If the side length is tripled, the area is multiplied by 9 and the volume is multiplied by 27.

Persevere with ProblemsSolvetheequationfor x.

20.(7x)3 = 7

15

SOLUTION:

Notice that the bases are the same. To solve for x in the exponent, find the value that makes the equation in the exponents equal.

21.(2m3n4)x = 8m9n12

SOLUTION:Simplify the first part of the equation.

Look at each of the terms on the left side of the equation and find the value of x that will make a true statement with the corresponding term on the other side of the equation.

(2)x = 8Thisistrueifx = 3.

m3x = m9Thisistrueifx = 3.

n4x = n

12Thisistrueifx = 3.

When x = 3, the terms are equal.

22.Which expression is equivalent to (104)8?

A. 102

B. 104

C. 1012

D. 1032

SOLUTION:

This corresponds with choice D.


23.(22)7


24.(8v9)5


25.(34)2


26.(m8)5


27.(z11

)5


28.[(43)2]2


29.[(23)3]2


30.(14y)4


Express the area of the square as a monomial.

31.

SOLUTION:Recall that the area of a square equals the measure

of one side squared, or A = s2. Use Power of a

Power to simplify the expression.

The area of the square is 64g6h

2 square units.

32.




The area of the square is 144d12

e14

square units.

Express the volume of the cube as a monomial.

33.

SOLUTION:Recall that the volume of a cube equals the measure

of one side cubed, or V = s3. Use Power of a Power

to simplify the expression.

The volume of the cube is 125r4s9 cubic units.

34.




The volume of the cube is 343m18

n27

cubic units.

Simplify.

35.(0.5k5)2


36.(0.3p 7)3


37.


38.PerseverewithProblemsA ball is dropped from

the top of a building. The expression 4.9x2 gives the

distance in meters the ball has fallen after x seconds.Write and simplify an expression that gives the

distance in meters the ball has fallen after x2

seconds. Then write and simplify an expression that

gives the distance the ball has fallen after x3

seconds.

SOLUTION:

Replace x with x2. Simplify.


39.What is the volume of the cube shown below?

A. 8m3

B. 16m5

C. 64m9

D. 512m9




This corresponds to choice D.

40.Which expression has the same value as 81h8k

6?

F. (9h6k4)2

G. (9h4k

3)2

H. (6h5k3)3

I.(3h2k)6

SOLUTION:Choice F:

This is not the same as the given expression. Choice G:

This is the given expression. Choice H:

This is not the same as the given expression. Choice I:

This is not the same as the given expression. So, the correct answer is G.

41.Which expression is equivalent to (2x2)5(5x6)?

A. 10x12

B. 80x12

C. 10x14

D. 80x14

SOLUTION:


42.ShortResponseManny has four pieces of carpet in the shape of a square like the one shown. He wants to use them together to carpet a portion of hisbasement. What is the area of the space he can cover with the carpet?


of one side squared, or A = s2. Use the Power of a

Product law to simplify the expression.

The area of the one of the squares is 4x4 square

units.Mannyhasfoursquaresofcarpet.44x4

=

16x4

SimplifyusingtheLawsofExponents.

43.646

7

SOLUTION:The common base is 6. Add the exponents.

44.183185


45.(3x11

)(6x3)

SOLUTION:Use the Commutative and Associative Properties to group the numbers and variables. The common base is x. Add the exponents.

46.(9a4)(2a7)

SOLUTION:Use the Commutative and Associative Properties to group the numbers and variables. The common base is a. Add the exponents.

47.The table shows the heights of some United States waterfalls. What is the height of each waterfall?

SOLUTION:Simplify each expression. Bridalveil:

The height of Bridalveil Falls is 620 feet. Fall Creek:

The height of Fall Creek Falls is 256 feet.Shoshone:

The height of Shoshone Falls is 212 feet.


1.(42)3


2.(53)3


3.(d7)6


4.(h4)9


5.[(32)2]2


6.[(52)2]2


7.(5j6)4


8.(11c4)3


9.(6a2b

6)3


10.(2m5n11)6


11.(3w3z

8)5


12.(5r4s12)4



measures 3c6d


cube as a monomial.

SOLUTION:



3c6d

2. Then simplify.



SOLUTION:




Then simplify.


12 cubic units.


15.


16.


17.(2v7)3(4v2)4




(a9)3


ofaPowerlaw.



5x2(7x



law.5x2(7x4)=5(7)x2 + 4 or 35x6



(n6)8





SOLUTION:a.



20.(7x)3 = 7

15

SOLUTION:


21.(2m3n4)x = 8m9n12





n4x = n




A. 102

B. 104

C. 1012

D. 1032

SOLUTION:



23.(22)7


24.(8v9)5


25.(34)2


26.(m8)5


27.(z11

)5


28.[(43)2]2


29.[(23)3]2


30.(14y)4



31.





2 square units.

32.





e14

square units.


33.





34.





n27

cubic units.

Simplify.

35.(0.5k5)2


36.(0.3p 7)3


37.








seconds.

SOLUTION:




A. 8m3

B. 16m5

C. 64m9

D. 512m9






6?

F. (9h6k4)2

G. (9h4k

3)2

H. (6h5k3)3

I.(3h2k)6

SOLUTION:Choice F:






A. 10x12

B. 80x12

C. 10x14

D. 80x14

SOLUTION:








=

16x4


43.646

7


44.183185


45.(3x11

)(6x3)


46.(9a4)(2a7)







eSolutions Manual - Powered by Cognero Page 1

1-4 Powers of Monomials


1.(42)3


2.(53)3


3.(d7)6


4.(h4)9


5.[(32)2]2


6.[(52)2]2


7.(5j6)4


8.(11c4)3


9.(6a2b

6)3


10.(2m5n11)6


11.(3w3z

8)5


12.(5r4s12)4



measures 3c6d


cube as a monomial.

SOLUTION:



3c6d

2. Then simplify.



SOLUTION:




Then simplify.


12 cubic units.


15.


16.


17.(2v7)3(4v2)4




(a9)3


ofaPowerlaw.



5x2(7x



law.5x2(7x4)=5(7)x2 + 4 or 35x6



(n6)8





SOLUTION:a.



20.(7x)3 = 7

15

SOLUTION:


21.(2m3n4)x = 8m9n12





n4x = n




A. 102

B. 104

C. 1012

D. 1032

SOLUTION:



23.(22)7


24.(8v9)5


25.(34)2


26.(m8)5


27.(z11

)5


28.[(43)2]2


29.[(23)3]2


30.(14y)4



31.





2 square units.

32.





e14

square units.


33.





34.





n27

cubic units.

Simplify.

35.(0.5k5)2


36.(0.3p 7)3


37.








seconds.

SOLUTION:




A. 8m3

B. 16m5

C. 64m9

D. 512m9






6?

F. (9h6k4)2

G. (9h4k

3)2

H. (6h5k3)3

I.(3h2k)6

SOLUTION:Choice F:






A. 10x12

B. 80x12

C. 10x14

D. 80x14

SOLUTION:








=

16x4


43.646

7


44.183185


45.(3x11

)(6x3)


46.(9a4)(2a7)








1.(42)3


2.(53)3


3.(d7)6


4.(h4)9


5.[(32)2]2


6.[(52)2]2


7.(5j6)4


8.(11c4)3


9.(6a2b

6)3


10.(2m5n11)6


11.(3w3z

8)5


12.(5r4s12)4



measures 3c6d


cube as a monomial.

SOLUTION:



3c6d

2. Then simplify.



SOLUTION:




Then simplify.


12 cubic units.


15.


16.


17.(2v7)3(4v2)4




(a9)3


ofaPowerlaw.



5x2(7x



law.5x2(7x4)=5(7)x2 + 4 or 35x6



(n6)8





SOLUTION:a.



20.(7x)3 = 7

15

SOLUTION:


21.(2m3n4)x = 8m9n12





n4x = n




A. 102

B. 104

C. 1012

D. 1032

SOLUTION:



23.(22)7


24.(8v9)5


25.(34)2


26.(m8)5


27.(z11

)5


28.[(43)2]2


29.[(23)3]2


30.(14y)4



31.





2 square units.

32.





e14

square units.


33.





34.





n27

cubic units.

Simplify.

35.(0.5k5)2


36.(0.3p 7)3


37.








seconds.

SOLUTION:




A. 8m3

B. 16m5

C. 64m9

D. 512m9






6?

F. (9h6k4)2

G. (9h4k

3)2

H. (6h5k3)3

I.(3h2k)6

SOLUTION:Choice F:






A. 10x12

B. 80x12

C. 10x14

D. 80x14

SOLUTION:








=

16x4


43.646

7


44.183185


45.(3x11

)(6x3)


46.(9a4)(2a7)










1.(42)3


2.(53)3


3.(d7)6


4.(h4)9


5.[(32)2]2


6.[(52)2]2


7.(5j6)4


8.(11c4)3


9.(6a2b

6)3


10.(2m5n11)6


11.(3w3z

8)5


12.(5r4s12)4



measures 3c6d


cube as a monomial.

SOLUTION:



3c6d

2. Then simplify.



SOLUTION:




Then simplify.


12 cubic units.


15.


16.


17.(2v7)3(4v2)4




(a9)3


ofaPowerlaw.



5x2(7x



law.5x2(7x4)=5(7)x2 + 4 or 35x6



(n6)8





SOLUTION:a.



20.(7x)3 = 7

15

SOLUTION:


21.(2m3n4)x = 8m9n12





n4x = n




A. 102

B. 104

C. 1012

D. 1032

SOLUTION:



23.(22)7


24.(8v9)5


25.(34)2


26.(m8)5


27.(z11

)5


28.[(43)2]2


29.[(23)3]2


30.(14y)4



31.





2 square units.

32.





e14

square units.


33.





34.





n27

cubic units.

Simplify.

35.(0.5k5)2


36.(0.3p 7)3


37.








seconds.

SOLUTION:




A. 8m3

B. 16m5

C. 64m9

D. 512m9






6?

F. (9h6k4)2

G. (9h4k

3)2

H. (6h5k3)3

I.(3h2k)6

SOLUTION:Choice F:






A. 10x12

B. 80x12

C. 10x14

D. 80x14

SOLUTION:








=

16x4


43.646

7


44.183185


45.(3x11

)(6x3)


46.(9a4)(2a7)








1.(42)3


2.(53)3


3.(d7)6


4.(h4)9


5.[(32)2]2


6.[(52)2]2


7.(5j6)4


8.(11c4)3


9.(6a2b

6)3


10.(2m5n11)6


11.(3w3z

8)5


12.(5r4s12)4



measures 3c6d


cube as a monomial.

SOLUTION:



3c6d

2. Then simplify.



SOLUTION:




Then simplify.


12 cubic units.


15.


16.

SOLUTION:To find the power of

Documents

Day 7 sept 12 mid chapter 1 check.notebook - …mrsdempseysmathsite.weebly.com/.../day_7_sept_12_… · · 2014-09-12Day 7 sept 12 mid chapter 1 check.notebook 3 ... H.O.T. Problems